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AuthorCercignani, Carlo. author
TitleThe Relativistic Boltzmann Equation: Theory and Applications [electronic resource] / by Carlo Cercignani, Gilberto Medeiros Kremer
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8165-4
Descript X, 384 p. online resource

SUMMARY

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation


CONTENT

1 Special Relativity -- 1.1 Introduction -- 1.2 Lorentz transformations -- 1.3 Tensors in Minkowski spaces -- 1.4 Relativistic mechanics -- 1.5 Electrodynamics in free space -- 2 Relativistic Boltzmann Equation -- 2.1 Single non-degenerate gas -- 2.2 Single degenerate gas -- 2.3 General equation of transfer -- 2.4 Summational invariants -- 2.5 Macroscopic description -- 2.6 Local Lorentz rest frame -- 2.7 Equilibrium distribution function -- 2.8 Trend to equilibrium. H-theorem -- 2.9 The projector ??? -- 2.10 Equilibrium states -- 3 Fields in Equilibrium -- 3.1 The general case -- 3.2 Non-degenerate gas -- 3.3 Degenerate relativistic Fermi gas -- 3.4 Degenerate relativistic Bose gas -- 4 Thermomechanics of Relativistic Fluids -- 4.1 Introduction -- 4.2 Thermodynamics of perfect fluids -- 4.3 Eckart decomposition -- 4.4 Landau and Lifshitz decomposition -- 4.5 Thermodynamics of a single fluid -- 5 Chapmanโ{128}{148}Enskog Method -- 5.1 Introduction -- 5.2 Simplified version -- 5.3 The integrals Il, I2 and I3 -- 5.4 Transport coefficients -- 5.5 Formal version -- 5.6 Appendix -- 6 Method of Moments -- 6.1 Introduction -- 6.2 Grad distribution function -- 6.3 Constitutive equations for Taร{159}ry and Paร{159} -- 6.4 Linearized field equations -- 6.5 Five-field theory -- 6.6 Maxwellian particles -- 6.7 Combined method of Chapmanโ{128}{148}Enskog and Grad -- 7 Chemically Reacting Gas Mixtures -- 7.1 Introduction -- 7.2 Boltzmann and transfer equations -- 7.3 Maxwellโ{128}{148}Jรผttner distribution function -- 7.4 Thermodynamics of mixtures -- 7.5 Transport coefficients -- 7.6 Onsager reciprocity relations -- 8 Model Equations -- 8.1 Introduction -- 8.2 The characteristic time -- 8.3 Single non-degenerate gas -- 8.4 Single degenerate gas -- 8.5 Relativistic ionized gases -- 8.6 Appendix -- 9 Wave Phenomena in a Relativistic Gas -- 9.1 Introduction -- 9.2 Propagation of discontinuities -- 9.3 Small oscillations -- 9.4 Shock waves -- 10 Tensor Calculus in General Coordinates -- 10.1 Introduction -- 10.2 Tensor components in general coordinates -- 10.3 Affine connection -- 10.4 Covariant differentiation -- 10.5 Spatial metric tensor -- 10.6 Special relativity in general coordinates -- 11 Riemann Spaces and General Relativity -- 11.1 Introduction -- 11.2 Tensors in Riemannian spaces -- 11.3 Curvature tensor -- 11.4 Physical principles of general relativity -- 11.5 Mechanics in gravitational fields -- 11.6 Electrodynamics in gravitational fields -- 11.7 Perfect fluids -- 11.8 Einsteinโ{128}{153}s field equations -- 11.9 Solution for weak fields -- 11.10 Exact solutions of Einsteinโ{128}{153}s field equations -- 11.11 Robertsonโ{128}{148}Walker metric -- 12 Boltzmann Equation in Gravitational Fields -- 12.1 Introduction -- 12.2 Transformation of volume elements -- 12.3 Boltzmann equation -- 12.4 Transfer equation -- 12.5 Equilibrium states -- 12.6 Boltzmann equation in a spherically symmetric gravitational field -- 12.7 Dynamic pressure in a homogeneous and isotropic universe -- 13 The Vlasov Equation and Related Systems -- 13.1 Introduction -- 13.2 The Vlasovโ{128}{148}Maxwell system -- 13.3 The Vlasovโ{128}{148}Einstein system -- 13.4 Steady Vlasovโ{128}{148}Einstein system in case of spherical symmetry -- 13.5 The threshold of black hole formation -- 13.6 Cosmology with the Vlasovโ{128}{148}Einstein system -- Physical Constants -- Modified Bessel Function


Physics Gravitation Astrophysics Physics Classical and Quantum Gravitation Relativity Theory Theoretical Mathematical and Computational Physics Astrophysics and Astroparticles



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